Specific count model for investing the related factors of cost of GERD and functional dyspepsia.

AIM: The purpose of this study is to analyze the cost of GERD and functional dyspepsia for investing its related factors.
BACKGROUND: Gastro-oesophageal reflux disease GERD and dyspepsia are the most common symptoms of gastrointestinal disorders. Recent studies showed high prevalence and variety of clinical presentation of these two symptoms imposed enormous economic burden to the society. Cost data that related to economics burden have specific characteristics. So this kind of data needs to specific models. Poisson regression (PR) and negative binomial regression (NB) are the models that were used for analyzing cost data in this paper. PATIENTS AND METHODS: This study designed as a cross-sectional household survey from May 2006 to December 2007 on a random sample of individual in the Tehran province, Iran to find the prevalence of gastrointestinal symptoms and disorders and its related factors. The Cost in each item was counted. PR and NB were carried out to the data respectively. Likelihood ratio test was performed for comparison between models. Also Log likelihood, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used to compare performance of the models.
RESULTS: According to Likelihood ratio test and all three criterions that we used to compare performance of the models, NB was the best model for analyzing this cost data. Sex, age and insurance statues were being significant.
CONCLUSION: PR and NB models were carried out for this data and according the results improved fit of the NB model over PR, it clearly indicates that over-dispersion is involved due to unobserved heterogeneity and/or clustering. NB model in cost data more appropriate fit than PR.

Introduction

Gastro-oesophageal reflux disease GERD is one of the most common symptoms of gastrointestinal disorders characterized by heartburn and/or acid regurgitation(1). Recent studies showed high prevalence and variety of clinical presentation of GERD imposed enormous economic burden to the society(2, 3). Another high prevalence gastrointestinal symptom is dyspepsia refers to a group of upper gastrointestinal symptoms. An international definition, Rom criterion is used for diagnosed of functional dyspepsia(4). However this disorder is not life threatening but the impact of this disorder on patient and society is considerable(5). Recently there are lots of study that investigated the economic burden of these symptoms worldwide(2, 3, 6–9). These studies have shown that the direct costs of GERD and dyspepsia ranged between PPP$172 (purchasing power parity dollars) and PPP$176 per person per year. Given the importance of affair, there are some studies for estimating of this economics burden in Iran recently. Rezai Lashkajani and Moghimi Dehkordi published their paper in 2007 and 2011 respectively (3, 9). On the other hand the continuing rise in charge for medical care worldwide has increased interest in precise estimating the cost of disease and the impact of specific treatments on the cost of care(10). So we have seen a heightened interest in studying the cost of health care, and medical cost data in recent years(11). Specific characterize of cost data is its distributions that are difficult to describe using standard approaches like ordinary least square regression for analyzing(12). Poisson model is one of the approach that use for analyzing such data like cost data. But due to over-dispersion, a related problem of Poisson regression, that arise in count data frequently, another model like Negative binomial use for this data(13). In this paper we use Poisson regression (PR) and negative binomial (NB) for analyzing the cost of GERD and dyspepsia.

Patients and Methods

This study was designed as a cross-sectional household survey from May 2006 to December 2007 on a random sample of individual in the Tehran province, Iran to find the prevalence of gastrointestinal symptoms and disorders and its related factors. Among this random sample, a total of 18180 adults (age > 18) were selected up (more details in refs (9, 23–29)). Then in the firs first step, trained health staff from the corresponding local health center contacted all selected random (18180), door to door and face to face, and asked them to participate in the interviews consisting of certain questionnaires. The research protocol of this study had been approved by the ethics committee of the Research Center for Gastroenterology and Liver Diseases, Shahid Beheshti University of Medical Science. The questionnaire was filled, was a valid and reliable questionnaire designed specifically for this study. This questionnaire included the symptoms of dyspepsia (23)(based on ROM III criteria), GERD (i.e. heartburn and regurgitation only) and their frequency in the last 6 month(27). In this questionnaire beside of information about listed symptoms, the frequency of the utilization of health services/resources including visits to physicians, drug intake, laboratory tests, hospitalizations and the productivity loss due to GERD/dyspepsia symptoms were reported. GERD was diagnosed as having heartburn or acid regurgitation on a weekly basis for the last 6 month. Dyspepsia was diagnosed, based on ROM III criteria, as a person who experienced one or more of the following symptoms for the past 3 month with symptoms onset at least 6 month before diagnosed. The symptoms as follow: bothersome postprandial fullness, early satiety, epigastric pain and epigastric burning sensation. The methodology of cost analysis in this study was similar to that other cost analysis in Iran(3, 30). In the calculation and analysis of cost, direct and indirect sources of expenses including physician's visit, drugs, laboratory test, hospitalization and day off work due to GERD- and dyspepsia –related symptoms were considered. The basic plans of the economic burden are as following:

Direct cost = physician visit + drug + laboratory test + hospitalization

Indirect cost = number of days with total productivity loss + number of days with at least 30% low functionality

Total cost = direct cost + indirect cost

All estimated costs were converted to PPP$, because of cross-country comparison. PPP$ is an economic technique for determine the relative values of two currencies(9).

Statistical methods

Frequency distribution and descriptive statistics such as mean, standard deviation and percentage were calculated according to standard methods. Outcome variable is the cost of GERD and dyspepsia. Two modeling approach were used for analyzing the relation between some demographic factors such as sex, age, marital status, education and other factors such as insurance status with cost of GERD and dyspepsia. The poisson regression (PR) is one of the models from general linear models (GLM) for describing count outcomes or proportion/rates(13). This model assumes response had a poisson distribution. Count data often vary more than we would expect if the response distribution truly were poisson. In this case the variances are much larger than the means, whereas Poisson distributions have identical mean and variance. The phenomenon of the data having greater variability than expected for a general linear model is called over-dispersion. A common cause of over-dispersion is heterogeneity among subjects(13). The negative binomial (NB), is another models from GLM as an alternative to the PR model, is a solution to account for over-dispersion due to unobserved heterogeneity (31). This model helps in adjusting the standard errors of the regression coefficients and provides a more flexible approach for prediction of the count outcome. To compare performance of the models, there are various methods such as log likelihood, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The p-values less than 5% were considered as significant results. All analysis was performed using STATA package.

Results

A total of 1929 patient were eligible and entered in this study. Of those in the study, 1186(61.4%) of patient had costs for gastrointestinal disorders. The mean and standard deviation of the costs per patient were 124.56 and 399.707 PPP$ respectively. Median of this cost was 47PPP$. The mean age was 46.22(standard deviation, 16.55) years and range 16-98 years.

The results of a univariate analysis of cost of GERD and dyspepsia between categorical variables are shown in Table 1. According to these results, there was a statistical significant difference between cost of GERD and dyspepsia in educational level, marital statues and insurance statues. But, there was not a statistically significant difference between male and female.

Table 1

Results of a univariate analysis of categorical variables

	Median	Range	p-value
Sex			0.342
Women	45	7230
Men	42	7614
Having insurance			<0.001
Yes	47	7614
No	38	7230
Marital statues			0.006
Single	35	1201
Widow	48	3534
Married	45	7614
Education			<0.001
Diploma or Upper diploma	36	7230
Lower diploma	48	7614

Finally PR regression and NB regression were performed for analyzing the relation between response and all factors simultaneously. In the PR model all covariates were significant.

The significant Pearson chi square goodness of fit (GOF) test (p < 0.001) along with other characteristics of model fit indicated that the PR model produced a poor fit for cost data. According the results of the NB model, age, sex and insurance statues had a significant relation with cost of patient. These results showed that gender of female (OR = 1.16; 95% CI 1.01, 1.36; P = 0.03) and high level of age (OR = 1.01; 95% CI 1.00, 1.02; P < 0.001) effected to increase the rate of costs. Beside for insured patient the rate of cost of their disease increased in compression of patient without insurance (OR = 1.16; 95% CI 1.00, 1.34; P = 0.04). On the other hand in this model, the estimated dispersion statistic (α) was 2.4 (95% CI: 2.29, 2.52). A significant likelihood ratio test (p < 0.001) of dispersion statistic from zero favored the NB model over the PR model. The model fit characteristics are shown in Table 2.

Table 2

Results of negative binomial model

Variable	Category	Estimation	SE	p-value	Odds ratio
Age		0.01	0.002	<0.001	1.01
Sex
	Women	0.14	0.06	0.018	1.16
	Men*	–	–		–
Having insurance
	Yes	0.14	0.06	0.04	1.16
	No*	–	–		–
Marital statues
	Single	–0.06	0.09	0.53	0.94
	Widow	0.04	0.11	0.66	1.04
	Married*	–	–
Education
	Upper diploma	–0.08	0.06	0.6	0.92
	Lower diploma*	–	–		–

Reference group

The entire Criterion showed that the NB model was better than PR model. Table 3 showed the results of 3 different criterions for comparison between NB and PR model.

Table 3

Comparison of model fit characteristics

	PR	NB
AIC*	575547.4	21307.6
BIC†	575585.9	21346.1
Logliklihood	−287766.7	−10646

Akaike Information Criterion

Bayesian Information Criterion

Discussion

Cost analyzing and related studies in clinical research, has been must attention in last years (10, 11). In this study we examined and analyzed the imposed cost of two high prevalence gastrointestinal symptoms in Tehran province population. This research was a part of a cross-sectional study that carried out in Tehran province in 2006 to 2007, aimed to determine the prevalence and related costs of some of the most common gastrointestinal disorder in this population(9, 24–28, 34, 35). GERD and dyspepsia are two common gastrointestinal disorders that have different prevalence in the world (1, 4, 5, 7, 8, 34, 36–40). According to this study the prevalence of GERD and dyspepsia was 8.85% and 8.5% respectively(23, 28). On the other hand the cost of GERD, dyspepsia and overlap of them was 111.4, 120.2 and 135 PPP$(9). So it seems that the cost of these disorders and the related factors that affecting these costs may be important. Special feature of cost data makes the data analysis is special(41). In another Iranian survey,

Cost analyzing and related studies in clinical research, has been must attention in last years (10, 11). In this study we examined and analyzed the imposed cost of two high prevalence gastrointestinal symptoms in Tehran province population. This research was a part of a cross-sectional study that carried out in Tehran province in 2006 to 2007, aimed to determine the prevalence and related costs of some of the most common gastrointestinal disorder in this population(9, 24–28, 34, 35). GERD and dyspepsia are two common gastrointestinal disorders that have different prevalence in the world (1, 4, 5, 7, 8, 34, 36–40). According to this study the prevalence of GERD and dyspepsia was 8.85% and 8.5% respectively(23, 28). On the other hand the cost of GERD, dyspepsia and overlap of them was 111.4, 120.2 and 135 PPP$(9). So it seems that the cost of these disorders and the related factors that affecting these costs may be important. Special feature of cost data makes the data analysis is special(41). In another Iranian survey,

The direct costs of GERD and dyspepsia have ranged fromPPP$172 to PPP$176 per person per year and comprised more than80% of the total cost of the disease. But this study was not population based, and the subjects were those referred to a gastroenterology clinic for upper endoscopy, their patients might have been suffering from relatively more severe or prolonged GERD and dyspepsia to be included in the cost analysis, which could cause an overestimation of the economic burden of illness compared with population studies such as ours (3).

The main feature is that the cost data are count. So modeling for cost data is needed. The first count model that researchers refer to it at the first is PR model. But because of the related problem of this model (over-dispersion), this model sometimes is not suitable and its results don't trust full. According to the results, the NB model and PR model have some differences with each other. In the PR model all the factors were significant. However in the NB model just 3 of them were significant. Besides, the likelihood ratio test in NB model showed that this data were over diapered. In this situation using PR model because the factors that not have significant effect will be significant by mistake.

According to the results of the goodness of fit, improved fit of the NB model over PR it clearly indicates that over-dispersion is involved due to unobserved heterogeneity and/or clustering. Also AIC, BIC and logliklihood criterion showed that NB model was better than the PR model. About related factors that they affected the costs, according to NB (the best model), female and older people had more cost than others. It seems this result was logic. Because according to previous our papers all of these factors (sex and age) are the risk factors of GERD and dyspepsia (23, 28). Some different, for example in inherent characteristics between men and women caused women had been cost more than men.

On the other hand having insured causes the rate of costs of patient increased significantly. The reason may be is that, patient that they do not have insurance, due to high costs of treatments and lack of financial ability, do not refer for treatment.